text: First let us note the definition of the advantage function: 
  
  $$A(s,a) = Q(s,a) - V(s) \; ,$$
  
  where $Q(s,a)$ is the action-value function and $V(s)$ is the state-value function. In theory you could represent these by two different function approximators, but this would be quite inefficient. However, note that 
  $$Q(s,a) = \sum_{s',r} \mathbb{P}(s',r|s,a)(r + V(s') = \mathbb{E}[r + V(s')|a,s]\;,$$
  so we can actually use a single function approximation, for $V(s)$, to completely represent the advantage function. To optimise this function approximator you would use the returns at each step of the episode as in e.g. the REINFORCE algorithm like you mentioned.